Abstract: This paper studies the sensitivity of posteriors to local and global perturbations of conjugate, shrinkage and sparsity priors. The perturbations are natural, geometrically motivated, and generalize the linear perturbation studied in Gustafson (1996). A geometric approach is also employed for optimizing the sensitivity direction function, which is defined on a convex space with non-trivial boundaries. The robustness of multi-dimensional models with shrinkage and sparsity priors is studied through simulation and through two real data sets; a benign breast disease study, and an adolescent placement study. Our results illustrate that there can exist significant sensitivity of the covariate coefficient estimates to perturbations of the independent weakly informative prior distributions.

Key words and phrases: Bayesian sensitivity, local mixture model, perturbation space, smooth manifold, shrinkage and sparsity priors.